Software

Primal-Dual Beltrami Regularization

The geometrically derived Beltrami framework, introduced by Sochen, Kimmel and Malladi (1998) offers an ideal compromise between feature preservation and avoidance of staircasing artifacts. Until now, one of the main limiting factors of the Beltrami regularizers was the lack of really efficient optimization schemes. Here, we start from one of the most efficient TV-optimization methods, primal-dual projected gradients, and apply it to the Beltrami functional. Doing so, we achieve better performance than ROF denoising for the basic grey-scale denoising problem, then extend the method to more involved problems such as inpainting, deconvolution, and the color case, all in a straightforward fashion. With the proposed primal-dual projected gradients optimization algorithm, the benefits of the geometric Beltrami regularizer become available at no extra computational cost, compared to state-of-the-art TV/ROF regularizers.

MATLAB Example

The MATLAB scripts/functions are included here to provide a way to illustrate the Beltrami algorithm.

Downloads – MATLAB scripts/functions demonstrating Beltrami denoising

• BELTRAMI_MATLAB.zip | DEMO | PAPER

When using the code, please refer to the following publication for documentation and as reference to be cited:

Reference

1. Zosso D, Bustin A. A Primal-Dual Projected Gradient Algorithm for Efficient Beltrami Regularization, UCLA CAM Report 14-52, 2014. [PDF]